Problem 16 - Chemistry: The Central Science in SI Units, Global Edition

Question

Write balanced chemical equations to correspond to each of the following descriptions: (a) When sulfur trioxide gas reacts with water, a solution of sulfuric acid forms. (b) Boron sulfide, \(\mathrm{B}_{2} \mathrm{~S}_{3}(s),\) reacts violently with water to form dissolved boric acid, \(\mathrm{H}_{3} \mathrm{BO}_{3},\) and hydrogen sulfide gas. (c) Phosphine, \(\mathrm{PH}_{3}(g)\), combusts in oxygen gas to form water vapor and solid tetraphosphorus decaoxide. (d) When solid mercury(II) nitrate is heated, it decomposes to form solid mercury(II) oxide, gaseous nitrogen dioxide, and oxygen. (e) Copper metal reacts with hot concentrated sulfuric acid solution to form aqueous copper(II) sulfate, sulfur dioxide gas, and water.

Step-by-Step Solution

Answer

(a) \(SO_3 + H_2O \rightarrow H_2SO_4\) (b) \(B_2S_3 + 6H_2O \rightarrow 2H_3BO_3 + 3H_2S\) (c) \(4PH_3 + 8O_2 \rightarrow 6H_2O + P_4O_{10}\) (d) \(2Hg(NO_3)_2 \rightarrow 2HgO + 4NO_2 + O_2\) (e) \(Cu + H_2SO_4 \rightarrow CuSO_4 + SO_2 + H_2O\)

Step 1: Write the unbalanced equation

The chemical formula for sulfur trioxide is SO₃, and for water it is H₂O. They react to form sulfuric acid (H₂SO₄). The unbalanced equation is: SO₃ + H₂O → H₂SO₄

Step 2: Balance the equation

The equation is already balanced: SO₃ + H₂O → H₂SO₄ (b) Boron sulfide reacts violently with water to form boric acid and hydrogen sulfide gas.

Step 1: Write the unbalanced equation

The chemical formula for boron sulfide is B₂S₃, and it reacts with water (H₂O) to form boric acid (H₃BO₃) and hydrogen sulfide gas (H₂S). The unbalanced equation is: B₂S₃ + H₂O → H₃BO₃ + H₂S

Step 2: Balance the equation

Balancing the equation gives us: B₂S₃ + 6H₂O → 2H₃BO₃ + 3H₂S (c) Phosphine combusts in oxygen gas to form water vapor and solid tetraphosphorus decaoxide.

Step 1: Write the unbalanced equation

Phosphine (PH₃) combusts in oxygen (O₂) to form water vapor (H₂O) and solid tetraphosphorus decaoxide (P₄O₁₀). The unbalanced equation is: PH₃ + O₂ → H₂O + P₄O₁₀

Step 2: Balance the equation

Balancing the equation gives us: 4PH₃ + 8O₂ → 6H₂O + P₄O₁₀ (d) Solid mercury(II) nitrate decomposes to form solid mercury(II) oxide, nitrogen dioxide, and oxygen.

Step 1: Write the unbalanced equation

When solid mercury(II) nitrate (Hg(NO₃)₂) is heated, it decomposes to form solid mercury(II) oxide (HgO), nitrogen dioxide (NO₂), and oxygen (O₂). The unbalanced equation is: Hg(NO₃)₂ → HgO + NO₂ + O₂

Step 2: Balance the equation

Balancing the equation gives us: 2Hg(NO₃)₂ → 2HgO + 4NO₂ + O₂ (e) Copper metal reacts with hot concentrated sulfuric acid solution to form aqueous copper(II) sulfate, sulfur dioxide gas, and water.

Step 1: Write the unbalanced equation

Copper (Cu) reacts with hot concentrated sulfuric acid (H₂SO₄) to form aqueous copper(II) sulfate (CuSO₄), sulfur dioxide gas (SO₂), and water (H₂O). The unbalanced equation is: Cu + H₂SO₄ → CuSO₄ + SO₂ + H₂O

Step 2: Balance the equation

Balancing the equation gives us: Cu + H₂SO₄ → CuSO₄ + SO₂ + H₂O

Key Concepts

Chemical Reactions

Chemical reactions are transformations that involve the rearrangement of atoms to form new substances. During a chemical reaction, the bonds between atoms in reactant molecules are broken and new bonds are formed in the product molecules. This results in different physical and chemical properties from the original substances.
Stoichiometry is central to chemical reactions. It involves balancing chemical equations to ensure the law of conservation of mass is obeyed, meaning that the number of each type of atom is the same on both the reactant and product sides. By balancing these equations, we can predict the quantities of reactants and products involved in the reaction.
For example, when sulfur trioxide (\(\text{SO}_3\)) reacts with water (\(\text{H}_2\text{O}\)) to form sulfuric acid (\(\text{H}_2\text{SO}_4\)), all atoms must be accounted for to balance the equation correctly, which is:

• \(\text{SO}_3 + \text{H}_2\text{O} \rightarrow \text{H}_2\text{SO}_4\)

Balancing chemical equations requires a systematic approach, often involving starting with more complex molecules and gradually balancing simpler atoms like hydrogen and oxygen.

Sulfuric Acid Formation

Sulfuric acid formation is an exothermic process where sulfur trioxide (\(\text{SO}_3\)) reacts with water (\(\text{H}_2\text{O}\)) to produce sulfuric acid (\(\text{H}_2\text{SO}_4\)). This reaction is crucial in industrial processes, especially in the manufacture of fertilizers, dyes, and explosives.
The overall reaction is very straightforward:

• \(\text{SO}_3 + \text{H}_2\text{O} \rightarrow \text{H}_2\text{SO}_4\)

Even though the equation is balanced as written, the actual reaction process involves a highly exothermic interaction, releasing a significant amount of heat.
This requires careful control to prevent hazards in industrial settings, where heat management is crucial to ensure safety and maximize efficiency.

Decomposition Reactions

Decomposition reactions are chemical changes where one compound breaks down into two or more simpler products. This type of reaction usually requires energy input, such as heat, light, or electricity, to break the chemical bonds in the reactant.
An example is the decomposition of mercury(II) nitrate (\(\text{Hg(NO}_3\text{)}_2\)) upon heating:

• \(2\text{Hg(NO}_3\text{)}_2 \rightarrow 2\text{HgO} + 4\text{NO}_2 + \text{O}_2\)

In this balanced decomposition reaction, mercury(II) nitrate breaks down into mercury(II) oxide (\(\text{HgO}\)), nitrogen dioxide (\(\text{NO}_2\)), and oxygen (\(\text{O}_2\)) gas.
The stoichiometry of decomposition reactions ensures the number of atoms is conserved during the transformation, illustrating the fundamental principle of conservation of mass.

Combustion Reactions

Combustion reactions are exothermic processes where a substance rapidly reacts with oxygen, releasing energy in the form of light and heat. These reactions are typically characterized by the presence of oxygen as a reactant and often involve hydrocarbons or more complex compounds.
An example is the combustion of phosphine (\(\text{PH}_3\)):

• \(4\text{PH}_3 + 8\text{O}_2 \rightarrow 6\text{H}_2\text{O} + \text{P}_4\text{O}_{10}\)

In this reaction, phosphine burns in oxygen to form water vapor and solid tetraphosphorus decaoxide (\(\text{P}_4\text{O}_{10}\)).
By balancing the combustion equation, we can determine the proportionate amounts of reactants and products, ensuring a complete and accurate description of the chemical change. Combustion reactions are vital in energy production, powering engines and other industrial processes through the controlled release of energy.